Related papers: Tame tori in p-adic groups and good semisimple ele…

Suppose $k$ is a nonarchimedean local field, $K$ is a maximally unramified extension of $k$, and $\mathbf{G}$ is a connected reductive $k$-group. If $\mathbf{T}$ is a $K$-minisotropic maximal $k$-torus in $\mathbf{G}$, then we use…

Let F be a non-archimedean local field of odd residual characteristic. Let G be a (connected) reductive group over F that splits over a tamely ramified field extension of F. We revisit Yu's construction of smooth complex representations of…

The Grothendieck--Serre conjecture predicts that every generically trivial torsor under a reductive group scheme $G$ over a regular local ring $R$ is trivial. We settle it in the case when $G$ is quasi-split and $R$ is unramified. Some of…

Let k be a local field and G the set of k-points of a connected semisimple algebraic k-group of rank one. We describe all torsion-free discrete subgroups of G\times G acting properly discontinuously on G by left and right multiplication. To…

Let G be a complex semisimple Lie group and H a complex closed connected subgroup. Let g and h be their Lie algebras. We prove that the regular representation of G in $L^2(G/H)$ is tempered if and only if the orthogonal of h in g contains…

We study compactifications of subvarieties of algebraic tori defined by imposing a sufficiently fine polyhedral structure on their non-archimedean amoebas. These compactifications have many nice properties, for example any k boundary…

Let $\mathbb F$ be a local field and $G$ be a linear algebraic group defined over $\mathbb F$. For $k\in\mathbb N$, let $g\to g^k$ be the $k$-th power map $P_k$ on $G(\mathbb F)$. The purpose of this article is two-fold. First, we study the…

A linear algebraic group G over a field k is called a Cayley group if it admits a Cayley map, i.e. a G-equivariant birational isomorphism over k between the group variety G and its Lie algebra Lie(G). A prototypical example is the classical…

In 2014, Reeder and Yu constructed epipelagic representations of a reductive $p$-adic group $G$ from stable functions on shallowest Moy-Prasad quotients. In this paper, we extend these methods when $G$ is split. In particular, we classify…

Let $G = Spec A$ be an affine $K$-group scheme and $\tilde{A} = \{w \in A*: dim_K A^* \cdot w \cdot A^* < \infty \}$. Let $< -,-> : A^* \times \tilde{A} \to K, (w,\tilde{w}) := tr(w \tilde{w})$, be the trace form. We prove that $G$ is…

We complete the proof of the Nisnevich conjecture in equal characteristic: for a smooth algebraic variety $X$ over a field $k$, a $k$-smooth divisor $D \subset X$, and a reductive $X$-group $G$ whose base change $G_D$ is totally isotropic,…

Answering a question of A. Rapinchuk, we construct examples of non- isomorphic semisimple algebraic groups H1 and H2 of type G2 with coherently equivalent systems of maximal k-tori.

For a rational prime p, let k be a perfect field of characteristic p, K be a finite totally ramified extension of Frac(W(k)) of degree e and r be a non-negative integer satisfying r<p-1. In this article, we prove the upper numbering…

For any number field K, it is unknown which finite groups appear as Galois groups of extensions L/K such that L is a maximal subfield of a division algebra with center K (a K-division algebra). For K=Q, the answer is described by the long…

In this paper we determine the precise extent to which the classical sl_2-theory of complex semisimple finite-dimensional Lie algebras due to Jacobson--Morozov and Kostant can be extended to positive characteristic. This builds on work of…

Let k be a complete, non-Archimedean field and let X be a k-analytic space ; assume that there exists a tamely ramified finite extension L/k such that X_L is isomorphic to an open polydisc over L ; we prove that X is itself isomorphic to an…

Suppose $G$ is a simple algebraic group defined over an algebraically closed field of good characteristic $p$. In 2018 Korhonen showed that if $H$ is a connected reductive subgroup of $G$ which contains a distinguished unipotent element $u$…

The paper concerns the topology of an isospectral real smooth manifold for certain Jacobi element associated with real split semisimple Lie algebra. The manifold is identified as a compact, connected completion of the disconnected Cartan…

In this article we give sufficient conditions for a group to have simple derived subgroup; the argument is based on generalising properties observed for extremely proximal micro-supported actions on the Cantor space, and generalises…

Let $\M(A,\theta)$ be a free partially commutative monoid. We give here a necessary and sufficient condition on a subalphabet $B\subset A$ such that the right factor of a bisection $\M(A,\theta)=\M(B,\theta\_B).T$ be also partially…